Dot-issar
 Veteran Build - Warhammer 40k: Darktide 

This build is mostly focused on leaning hard into your damage over time opportunities. Veteran as a character is absurdly good at building up dots fast and effectively, and this build allows that, while still staying mobile enough to get in and out for revives.

The Heavy Laspistol Mk. II offers two primary problem solvers: Aiming down sights has decent cleave and overall damage on weakspot hits, chipping into hordes while keeping your distance. Along with that, you can rapidly fire to apply stacks of burn, namely against more threatening foes that the damage itself can't outright put down, namely maulers, scab ragers, crushers, mutants, and bosses. 

If you're not a fan, the Recon Lasgun with similar 60 in stability 80 otherwise offers a viable alternate. Take 5% crit strike chance and 25% unyielding damage for your perks, and infernus with headhunter for your blessings. It should fill the same roles while offering alternative combat feel.

The Combat Blade Mk. VI follows the same philosophy as your ranged option. You can sweep with lights, offering heavy bleed potential on effectively any enemy. Don't be discouraged by armor effects, bleed's impact simply requires contact, not penetration. Your approach changes slightly for larger enemies, applying the bleed up to cap, then switching to targeting weakspot. While you will lose out on bleed stacks slowly, you strikes to the weakspot will apply 16 stacks of brittleness, allowing for a massive increase in both your bleed and burn damage, along with assistance for your team overall.

For an alternative that offers a bit more horde clear, I recommend the Power Falchion Mk. I. With 5% melee crit chance and flak damage for the perks, and Cranial Grounding and Heatsink for the Blessings, you simply power up, aim for weakspots, and sweep. Without perks directly into melee combat, you wont feel the Power Falchion's full potential, but it should be plenty to keep major threats off you. If you go this route, i recommend dropping serrated blade for the 15% damage node above your keystones, as you'll want the raw power over minor bleed benefits. 

The biggest benefit of this build would be it's support capabilities. As expected with a shout veteran, your ability to apply goal toughness is unmatched, allowing for emergency saves or pre-prepped pushes into hordes that your team would otherwise not be able to come out of unscathed. While it might've been previously not worth taking the ability to revive on shout, recent updates have allowed it to not cost you a weakened coherency range, meaning this can and will save your team at the low, low cost of a single skill point.

If you don't want the shout, it's recommended you either take Kraks instead of Shredder Grenades, with the Grenade Tinkerer perk, or simply the grenadier perk with your current Shredder Grenades. The Veteran's ability to actively regenerate grenades gives them yet another out that other classes don't have from dangerous situations.